Abstract:

The datasets illustrate the effect of prey evolution on the predator-prey dynamics through numerical simulation. These numerical examples help us understand how toxicant exposure and the prey evolution to resist toxicants may have a significant impact on the dynamical outcomes of a predator-prey system. In particular, the datasets for example 4.1 in the manuscript illustrates what happens to the populations when the initial toxicant effect is fixed at a low, intermediate, and high level. This example shows the time-series population densities of prey and predator values and gives the measure of the amount of toxicant resistance that the prey population evolves. In addition, example 4.2 provides long-time dynamics of the population equilibrium values of prey, predator, and the mean trait value of prey evolution (toxicant resistance) for different prey growth rate independent of the environment (i.e. r_0) when the initial toxicant level varies over the range 0≤ϵ_0≤1 instead of fixing ϵ_0 at a low, intermediate, or high level. This example provides the equilibrium densities of prey and predator populations as a function of the initial level of toxicant ϵ_0 with a step size of 0.01 ranging from 0 to 1. Combined, these two examples show that both prey and predator populations may survive in higher initial toxicant levels with evolution compared to when there is no evolution. Also, both species may go extinct for lower toxicant levels when, prior to evolving toxicant resistance, the prey’s inherent growth rate is small. This dataset supports the publication: Ackleh, A. S., Hossain, M. I., Veprauskas, A., & Zhang, A. (2019). Persistence and stability analysis of discrete-time predator–prey models: a study of population and evolutionary dynamics. Journal of Difference Equations and Applications, 25(11), 1568–1603. doi:10.1080/10236198.2019.1669579.

Suggested Citation:

Ackleh, Azmy S.. 2021. Dataset for: Persistence and stability analysis of discrete-time predator–prey models: a study of population and evolutionary dynamics. Distributed by: GRIIDC, Harte Research Institute, Texas A&M University–Corpus Christi. doi:10.7266/JKBQ0YZ5

Publications:

Ackleh, A. S., Hossain, M. I., Veprauskas, A., & Zhang, A. (2019). Persistence and stability analysis of discrete-time predator–prey models: a study of population and evolutionary dynamics. Journal of Difference Equations and Applications, 25(11), 1568–1603. doi:10.1080/10236198.2019.1669579

Purpose:

Understand how toxicant exposure and the prey evolution to resist toxicants may significantly impact the dynamical outcomes of a predator-prey system based on numerical simulation.

Data Parameters and Units:

T: time (hours, days, years, etc.), n(t): prey density (numbers of prey per unit area), p(t): predator density (number of predators per unit area), u(t): prey population mean trait describing the amount of toxicant resistance possessed by prey when prey is evolving to toxicant resistance. eps0 (called ϵ_0): initial level of the toxicant present in the environment. The dataset includes the codes used to reproduce figures in the associated publication Ackleh et al., 2019.

Methods:

Dataset contains numerical simulation. For the detailed methods, please refer to the associated Ackleh et al., 2019.

Individual Files: